
\(\mathrm {F}_i \in \mathbb {R}^{H, W, F}\)  is the feature map of the \(i^{th}\)  instance. \(H, W, F\)  are the height, width and feature dimension respectively. \(j \in \lbrace 1, \dots , W\rbrace , k \in \lbrace 1, \dots , H\rbrace \)  and \(n_t\)  is the number of target instances in the dataset. This is exactly what is done in several recent domain adaptation works [1]}, [2]}, where we have access to a target training set on which we can estimate distribution statistics. However, in our setting, we do not have access to such a train set from the target distribution. In fact, we need to adapt to one test instance at a time, and cannot use the updated model or the current instance's statistics to infer the subsequent test instances. This makes our setting much harder compared to other settings in literature on test time adaptation [3]}.
